How to extract a signal of Z decays to b-jets February 19, 2007

In a recent post I promised I would discuss the analysis by which the CDF collaboration (that is, Julien and me, in this case!) extracts a signal of Z decays to b-quark-jet pairs… So here it goes.

The process of Z production, followed by the decay of the weak Z boson to b-quark pairs, occurs roughly once every fifty million times at the Tevatron. This fact would not be disheartening by itself – signals a thousand times rarer can and have been isolated – were it not for the additional complication that the signature produced by two b-quarks emitted by the Z is really not very distinctive: a pair of back-to-back jets which contain hints of the decay of B-hadrons. The lack of tale-telling features capable of distinguishing the Z event from the 49,999,999 other collisions is the real trouble in extracting a Z–>bb decay!

The CDF online data selection is a set of hardware devices that read in the detector output and decide in real time whether a proton-antiproton collision is worth writing to disk or not. While the collision rate is 3 millions per second, the storage system can only write to disk 100 events per second or so: a very selective filter, the trigger, takes care of picking the most interesting ones and discarding the rest. The search for Z->bb decays starts right there, at the trigger selection: to ensure that they get collected, the trigger must somehow recognize them.

An extraordinary device called the SVT takes care of precisely reconstructing the trajectories of charged tracks contained in jets in microseconds, allowing the trigger to select jet production events where b-quarks are likely to be present.

Due to the need of reducing the huge rate of QCD processes yielding b-quark jets in the final state as well as light-quark or gluon jets mistaken by the SVT as coming from b-quarks, the trigger selection kills 95% of our beloved events. We have to live with this, and be happy of the 5% we have a chance to study. [Note: QCD (quantum chromo-dynamics) processes are those mediated by the strong interaction. Most frequently, they consist in a high-energy scattering of two quarks or gluons off one another. The scattered bodies hadronize in a pair of back-to-back jets not unlike those from Z decay.]

The surviving events are reconstructed by an offline program, and then a further filtering starts: we need to get rid of as much background as we can, by relying on any conceivable characteristics able to discriminating Z production from QCD events.

The selection starts off by requiring both jets to contain a reconstructed secondary vertex. A secondary vertex is the originating point of two or more charged tracks contained in the jet cones, and it is the result of the long lifetime of the b-quark. The hadron containing the b-quark leaves the primary interaction point at little less than light speed, traveling as much as a few millimeters before disintegrating into the charged particles which allow to determine the decay point.

After the selection of an almost pure b-quark pair production final state, the signal-to-noise ratio is still very small: in the data analyzed by CDF, about 10,000 Z->bb events are contained in dataset of about a million events. But QCD events, produced by strong interactions, are different from Z production, due to weak interactions. The difference is that the Z can only be produced by the collision of two quarks – one from the proton and one from the antiproton-, while QCD events are mostly the result of a gluon-gluon collision -again, each coming from one of the two colliding bodies.

Gluons, the mediators of the strong force, have a higher color charge than quarks. They are thus more likely to radiate additional gluons. This is a difference that results in a higher fraction of three-jet events in QCD processes than in Z production processes. For the same reason, the two leading jets emitted from the Z decay are more likely to be back-to-back than jet pairs from QCD events.

A selection tuned to increase as much as possible the signal significance is thus performed on two kinematic variables: the angle between the two jets, which is required to be close to 3.14, and the transverse energy carried by the third jet in the event – if there is any. This allows the signal to noise ratio to become roughly 2% – a Z event every 50 QCD events.

Once you have done all you can to increase the signal significance, you have one last weapon – the most powerful one, which you saved for your advertising plot. It is the invariant mass of the dijet system: when the Z boson decays to two b-jets, it imparts them with energy equal to its rest mass. By measuring the energy of the two b-jets you can get back the 91 GeV of the Z mass, give or take some uncertainty due to the imprecise determination of jet energy. QCD events, on the other hand, are not the result of a massive particle decay: the reconstructed mass of b-jets from QCD processes is a smoothly falling distribution, whose shape reflects the selection cuts (requiring jets to have energy in excess of 20 GeV, say) and the decreasing probability of higher energy collsions.

The plot shown above is the final result of the analysis performed on early Run II data in 2005. The Z contribution extracted by a two-component fit is shown in green. You can see that it is a small fraction of the total data! Yet, its measurement carries some significance, because by comparing the result with simulations we learn how well we measure the jet energy in our detector.

In four days, Julien will bless the result of our analysis of new data – almost twice as much as the data shown in the plot above. From the Z signal we have successfully extracted a measurement of our b-jet energy scale, which carries an uncertainty as small as the best determination obtained so far with the W->jj signal in top pair production events.

So what is the big deal ? Well, this determination of the b-jet energy scale is the first ever obtained with b-quarks. The W signal allows to set the energy scale of light quark jets, which are potentially quite different. With this new measurement, the future top quark mass measurements at the Tevatron will sizably decrease their systematic uncertainty.

I will say something more when I will have permission to be more quantitative… After the blessing!